Category:Lipschitz Spaces

This category contains results about Lipschitz Spaces.

Let $\struct {X _\mathbf A, \sigma_\mathbf A}$ be a shift of finite type.

Let $\theta \in \openint 0 1$.

The Lipschitz space on $X _\mathbf A$ with respect to the metric $d_\theta$ is defined as:

$\ds \map {F_\theta} {X_\mathbf A} := \set {f \in \map C {X _\mathbf A, \C} : \sup_{n \mathop \in \N} \dfrac {\map {\mathrm {var}_n} f} {\theta^n} < \infty}$

where:

$\map C {X _\mathbf A, \C}$ denotes the continuous mapping space

$\mathrm {var}_n$ denotes the $n$th variation